Computer vision and remote sensing applications often utilize motion determination from an image sequence for video coding or other purposes. The determination of a displacement or motion field under brightness or tracer conservation constraints from an image sequence has thus far been considered an under-constrained problem. In general, the determination of the instant velocities from an image sequence or a physical displacement field from a featureless image sequence is ill-posed. Conventional motion estimation involves finding a velocity or displacement field using successive image frames, and existing motion estimation models and algorithms assume that the image intensity recorded from different physical sensors obey a conservation constraint for tracer, heat, or optical flow in space and time.
The inverse problem of the determination of the motion field under brightness (or tracer) conservation constraint from an image sequence has been considered as an under-constrained problem because two unknown velocity components must be derived from a single conservation equation at each of these pixel points, which is sometimes referred to as the aperture problem. The aperture problem indicates that the physical observation may not be consistent with the physical motion if there are not enough texture structures on moving objects. The physical determination of a displacement vector in a featureless image sequence is ill-posed, but this texture dependent problem is different from the under-constrained problem. In the past, the under-constrained problem has been addressed by using different models or frameworks with additional constraints and assumptions. For instance, Pel-Recursive techniques have been proposed, and differential techniques have been proposed using regularization, uniform velocity in a block (template), gradient conservation, and velocity field modeling with bilinear or B-spline type constraints. In addition, Bayesian methods have been proposed in which the motion field is modeled as a Markovian random field. However, these conventional techniques suffer from computational inefficiencies and inaccuracies which can lead to errors in video coding and other computer vision and remote sensing applications. Accordingly, a need remains for improved methods and apparatus for processing image sequence data to determine displacement by motion compensation.